Will a character work well with animation if it wasn't made with t-pose?
I would not stick to a concept if it doesn't fit your needs. If your character's limbs can't even reach t-pose it's moot anyways. The main issue you might run into is axis alignment. It is a good idea to stick to 1 axis for bone directions, but it can't ever be possible in a complex character.
If your character's rest pose is different from the t-pose, use the one that's closest to what the char. does most of times. But note that IK constraints are easier to set up in t-pose.
I would suggest using none-t-pose and pose a few extremes, if there's no problem, there likely won't be one in the future.